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The dichotomy paradox
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
This description requires one to complete an infinite number of steps, which for Zeno is an impossibility. This sequence also presents a second problem in that it contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion.
Originally posted by MysticalUnicorn
Ok, I used to be an ATS veteran, but now I am turned noobie. I left the board for a sports board. Anyways, I apologize if someone already came up with this question!
People have been talking about big things, and one of my theories is going to rock our worlds! Bear with me!
Let's say I am going to the kitchen to get a sandwich. I am 50 feet from the fridge. How can I get to the kitchen if the space can be infinitly divided? This either questions the truth of fractions or the truth of infinity, or perhaps something else.
Another scenario. How does time move. How can a second be called a second when there are infinite decimal points. Where is Brian Greene when you need him!
Originally posted by Xar Ke Zeth
And regarding irrational numbers, that's just how they are. [....] I'm not sure what question you posed....